Russia will continue to press for a peaceful resolution of the Nagorno-Karabakh conflict, President Vladimir Putin said on Wednesday after holding talks in Moscow with his Armenian counterpart Serzh Sarkisian.

Putin, who also met with Azerbaijani President Ilham Aliyev on Monday, insisted that both Armenia and Azerbaijan are committed to a compromise settlement but would not say whether it can be achieved in the coming months.

“We will continue to provide the utmost support to the search for ways of untying the ‘Karabakh knot’ within the framework of the OSCE Minsk Group as well as during direct contacts with Yerevan and Baku,” he told a news conference with Sarkisian.

“We hope that Armenia and Azerbaijan will manage to reach a compromise settlement -- without winners or losers -- of existing differences,” he said.

Putin said that he and Sarkisian paid “serious attention” to the Karabakh issue at their talks, including through the prism of the most recent meeting of the Armenian and Azerbaijani presidents which the Russian leader hosted in Saint Petersburg on June 20.

In a joint statement with Putin issued in Saint Petersburg, Aliyev and Sarkisian said they reached “understandings” on unspecified issues hampering a Karabakh settlement. Russian Foreign Minister Sergey Lavrov said afterwards that the conflicting parties are now closer to cutting a peace deal than ever before.

The Armenian press has since been rife with speculation that Moscow is pressing the Armenian side to agree to withdraw from five of the seven districts around Karabakh that were fully or partly occupied by Karabakh Armenian forces during the 1991-1994. Some commentators in Yerevan have pointed to statements to that effect made by Azerbaijani officials.

Putin did not confirm the Azerbaijani claims, implying that they only reflect Armenian concessions that are sought by Baku. He also said in that regard: “I think that both Armenia and Azerbaijan really want to find a way out of the problem in order to live in peace, cooperate and develop the economy.”

In particular, he said, a Karabakh peace would lead to economic betterment in Armenia and thereby “strengthen Armenian statehood.”

“But we need to find the kind of approaches and formulas that would not leave anybody thinking that they have lost or won, a solution that would be worked out by Armenia’s and Azerbaijan’s leaders and accepted by the publics in both countries,” Putin went on. Russia and other mediating powers are ready to act as “guarantors” of such an accord, he added.

Sarkisian, for his part, stressed that an Armenian-Azerbaijan peace accord can only be based on the Karabakh Armenians’ right to self-determination. “This is what I discussed with the president of the Russian Federation in detail today,” he said.

Neither Putin nor Sarkisian publicly commented on the possibility of organizing another Armenian-Azerbaijani summit which the mediators hope would result in further progress in the Karabakh peace process. French President Francois Hollande reportedly offered to host it in Paris shortly after the Saint Petersburg meeting.

Sarkisian praised Putin’s peace efforts in his opening remarks at the talks held in the Kremlin. “In this regard, it is very, very important that all reached agreements are fulfilled,” he said. “We are prepared for that.”

Azerbaijan -- Russian President Vladimir Putin (L) speaks with Azerbaijani President Ilham Aliyev during their meeting in Baku, August 8, 2016

The Armenian president may have referred to safeguards against renewed ceasefire violations which he and Aliyev agreed to take at their previous meeting held in Vienna on May 16, more than a month after the worst escalation of the conflict since 1994. Yerevan subsequently accused Baku of trying to walk away from those agreements.

Putin discussed the Armenian-Azerbaijani dispute with Aliyev when he visited Baku on Monday. He told Sarkisian that he “would love to brief you on the results of our meetings in Baku.”

Speaking at the ensuing news conference, Putin dismissed a widely held belief in Armenia that Russia has only increased the risk of another Karabakh war with its large-scale arms sales to Baku. He implied that oil-rich Azerbaijan would have been able to purchase offensive weapons from other nations had Russia refused to sign defense contracts, reportedly worth $4 billion, with it in 2010-2011.

Putin also argued that Russia has long been providing substantial military aid to Armenia, its main regional ally. Moscow “always fulfills its obligations” to Yerevan relating to defense, he said.